Given :

• Volume of cylinder = 6160 cm³
• Height of the cylinder = 10 cm

To find :

• Radius of the cylinder
• TOTAL surface area of cylinder

Concept :

➳ Formula of volume of cylinder :-

• Volume of cylinder = πr²h

➳ Formula to calculate total surface area of cylinder :-

• TSA of cylinder = 2πr(r + h)

where,

• Take π = 22/7
• r = radius
• h = height

Solution :

Using formula,

✭ Volume of cylinder = πr²h

Substituting the given values,

⇒ 6160 = 22/7 × (r)² × 10

⇒ 6160 = 220/7 × r²

⇒ 6160 × 7/220 = r²

⇒ 616 × 7/22 = r²

⇒ 308 × 7/11 = r²

⇒ 28 × 7 = r²

⇒ Taking square root on both the sides.

⇒ √(2 × 2 × 7 × 7) = r

⇒ ± 2 × 7 Reject - ve = r

⇒ 14 = r

The value of r = 14.

◈ Radius of the cylinder = 14 cm

Using formula,

✭ TSA of cylinder = 2πr(r + h)

Substituting the given values,

⇒ TSA = 2 × 22/7 × 14(14 + 10)

⇒ TSA = 2 × 22 × 2(24)

⇒ TSA = 2,112

◈ Total surface area of cylinder = 2,112 cm²

━━━━━━━━━━━━━━━━━━━

Some related formulae ::

• Diameter = 2 × Radius
• Radius = Diameter ÷ 2
• Area of circle = πr²
• Circumference = 2πr
• Volume of cone = 1/3 πr²h
• Curved surface area of cone = πrl
• Total surface area of cone = πrl + πr²h
• Surface area of sphere = 4πr²
• Volume of cylinder = πr²h